Interferometric techniques are widely used to obtain the real-time phenomena in a majority of applications considering its advantages of non-intrusively, mapping changes in path length as small as the wavelength of the light source used, etc. Interferometers often recorded the changes in the path length in the form of fringe orientation. Depending upon the complexity of the phenomena under observation, interferometric fringes are formed from simple fringe ordinations to complex fringe structures. Extracting phase map from these fringe patterns are highly crucial to evaluate the phase change and the corresponding property change. In order to use the interferometers in its full potential, it is necessary to develop robust and accurate algorithms for phase extraction. In this paper, we discuss 2-D Hilbert transforms (HT) and 2-D continuous wavelet transforms (CWT) techniques to analyze fringe patterns of different orientation and inter-fringe spacing. Simulated interferograms were used to generate implemented fringe patterns with different orientation and spacing. MATLAB software is used to generate these simulated image. In order to check the efficiency of the mentioned algorithm, a white Gaussian filter with different noise levels (0%, 5%, 10%) has been added to the simulated interferograms. Interferometric fringes with noise is a common phenomenon in many transient and turbulent processes. Moreover, the in-build noise in optical configuration and external noises in the testing environment also adds to the noise. Hence, it is necessary to test the accuracy of algorithm for enhanced noises. The results show that the HT algorithm was difficult to implement on complex patterns and was also difficult to implement for a high degree of noise interference. The two-dimensional CWT, on the other hand, has good performance on complex striped patterns and can handle noise disturbances with a good degree of accuracy. The continuous wavelet transform is insensitive to noise interference patterns and gives accurate results. The processing time is very short and it can handle both simple and complex fringe patterns within a very short period of time. It can also be concluded that the 2-D CWT algorithm is very effective and robust.

考虑到其非侵入性、映射路径长度的变化与所使用的光源的波长一样小等优点，干涉仪技术被广泛用于在大多数应用中获取实时现象。干涉仪通常记录光程的变化。以条纹方向形式表示的路径长度。根据观察现象的复杂性，干涉条纹由简单的条纹排列到复杂的条纹结构形成。从这些条纹图案中提取相图对于评估相变和相应的属性变化非常重要。为了充分发挥干涉仪的潜力，有必要开发稳健且准确的相位提取算法。在本文中，我们讨论二维希尔伯特变换（HT）和二维连续小波变换（CWT）技术来分析不同方向和条纹间距的条纹图案。模拟干涉图用于生成具有不同方向和间距的实施条纹图案。MATLAB 软件用于生成这些模拟图像。为了检查上述算法的效率，在模拟干涉图中添加了具有不同噪声级别（0%、5%、10%）的白高斯滤波器。带有噪声的干涉条纹是许多瞬态和湍流过程中的常见现象。此外，光学配置中的内置噪声和测试环境中的外部噪声也会增加噪声。因此，有必要测试增强噪声算法的准确性。结果表明，HT算法在复杂图案上难以实现，在噪声干扰程度较高的情况下也难以实现。另一方面，二维连续小波变换在复杂的条纹图案上具有良好的性能，并且能够以良好的精度处理噪声干扰。连续小波变换对噪声干扰模式不敏感，并给出准确的结果。处理时间非常短，可以在很短的时间内处理简单和复杂的条纹图案。还可以得出结论，2-D CWT 算法非常有效且鲁棒。